Much of the development of economic theory has been based on assumptions that credit economic agents with perfect discriminating power and perfect consistency in their choice behavior, but recently a range of less restrictive psychological choice theories has been introduced into economic analysis. These theories may be classed into two types--those that treat preference (and hence choice) as a probabilistic phenomenon, and those that retain the deterministic structure of the traditional analysis but relax in some way the assumption that individual preference be transitive. In previous work other have examined the implications for economic equilibrium of asuming preferences to be random; our purpose in this paper is to examine the equilibrium implications of a particularly attractive deterministic choice theory, that of semiordered preferences. We first examine an exchange economy in which the agents' preferences are semiorders that are not too nonconvex; such an economy is shown to have an equilibrium, and further, for interior equilibria, it is shown that a range of allocations to consumers is consistent with equilibrium. Finally, we show that in a semiorder market economy the set of price equilibria has a non-empty interior relative to the price simplex.